(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     38570,       1036]
NotebookOptionsPosition[     34575,        912]
NotebookOutlinePosition[     36888,        974]
CellTagsIndexPosition[     36768,        968]
WindowTitle->CTdec
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"Tdec\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/Tdec"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/CTdec\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/CTdec"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/CTdec.\
html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> 
            False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$53720], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], "FeynCalc/ref/CTdec",
              ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["CTdec", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"CTdec", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"qi", ",", "a"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"qj", ",", "b"}], "}"}], ",", "..."}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"p1", ",", "p2", ",", "..."}], "}"}]}], "]"}]], 
      "InlineFormula"],
     " \[LineSeparator]or CTdec[exp, {{qi, a}, {qj, b}, ...}, {p1, p2, ...}] \
calculates the tensorial decomposition formulas for Cartesian integrals. The \
more common ones are saved in TIDL."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->296209834],

Cell["", "SectionHeaderSpacer"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "CTdec", "]"}]], "Input",
 CellLabel->"In[214]:=",
 CellID->131732672],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"FeynCalc`Package`BasisOnly", "\[Rule]", "False"}], ",", 
    RowBox[{"Dimension", "\[Rule]", 
     RowBox[{"D", "-", "1"}]}], ",", 
    RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", 
    RowBox[{"Factoring", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"Factor2", ",", "Factor"}], "}"}]}], ",", 
    RowBox[{"FeynCalcExternal", "\[Rule]", "True"}], ",", 
    RowBox[{"List", "\[Rule]", "True"}], ",", 
    RowBox[{"UseParallelization", "\[Rule]", "True"}], ",", 
    RowBox[{"UseTIDL", "\[Rule]", "True"}]}], "}"}], 
  TraditionalForm]], "Output",
 ImageSize->{470, 54},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[214]=",
 CellID->1788246199]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->380288136],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->1709125748],

Cell[TextData[{
 "Check that ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"\[Integral]", 
     RowBox[{
      SuperscriptBox["d", 
       RowBox[{"D", "-", "1"}]], 
      RowBox[{"f", "(", 
       RowBox[{"p", ",", "q"}], ")"}], 
      SuperscriptBox["q", "i"]}]}], "=", " ", 
    RowBox[{
     FractionBox[
      SuperscriptBox["p", "i"], 
      SuperscriptBox["p", "2"]], 
     RowBox[{"\[Integral]", 
      RowBox[{
       SuperscriptBox["d", 
        RowBox[{"D", "-", "1"}]], 
       RowBox[{"f", "(", 
        RowBox[{"p", ",", "q"}], ")"}], 
       RowBox[{"p", "\[CenterDot]", "q"}]}]}]}]}], TraditionalForm]]]
}], "Notes",
 CellID->76274125],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"CTdec", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"{", 
     RowBox[{"q", ",", "i"}], "}"}], "}"}], ",", 
   RowBox[{"{", "p", "}"}]}], "]"}]], "Input",
 CellLabel->"In[1]:=",
 CellID->272441690],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"X1", "\[Rule]", 
       FormBox[
        RowBox[{
         FormBox[
          FormBox[
           StyleBox["p",
            StripOnInput->False,
            FontWeight->Bold],
           TraditionalForm],
          TraditionalForm], 
         FormBox["\<\"\[CenterDot]\"\>",
          TraditionalForm], 
         FormBox[
          FormBox[
           StyleBox["q",
            StripOnInput->False,
            FontWeight->Bold],
           TraditionalForm],
          TraditionalForm]}],
        TraditionalForm]}], ",", 
      RowBox[{"X2", "\[Rule]", 
       FormBox[
        SuperscriptBox[
         FormBox[
          FormBox[
           StyleBox["p",
            StripOnInput->False,
            FontWeight->Bold],
           TraditionalForm],
          TraditionalForm], "2"],
        TraditionalForm]}]}], "}"}], ",", 
    FractionBox[
     RowBox[{"X1", " ", 
      FormBox[
       SuperscriptBox[
        FormBox[
         FormBox[
          StyleBox["p",
           StripOnInput->False,
           FontWeight->Bold],
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox[
          StyleBox["i",
           StripOnInput->False,
           FontWeight->Bold],
          TraditionalForm],
         TraditionalForm]],
       TraditionalForm]}], "X2"]}], "}"}], TraditionalForm]], "Output",
 ImageSize->{231, 39},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]=",
 CellID->1870429102]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"%", "[", 
   RowBox[{"[", "2", "]"}], "]"}], "/.", 
  RowBox[{"%", "[", 
   RowBox[{"[", "1", "]"}], "]"}]}]], "Input",
 CellLabel->"In[2]:=",
 CellID->1508196487],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    FormBox[
     SuperscriptBox[
      FormBox[
       FormBox[
        StyleBox["p",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["i",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]],
     TraditionalForm], " ", 
    RowBox[{"(", 
     FormBox[
      RowBox[{
       FormBox[
        FormBox[
         StyleBox["p",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm], 
       FormBox["\<\"\[CenterDot]\"\>",
        TraditionalForm], 
       FormBox[
        FormBox[
         StyleBox["q",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]}],
      TraditionalForm], ")"}]}], 
   FormBox[
    SuperscriptBox[
     FormBox[
      FormBox[
       StyleBox["p",
        StripOnInput->False,
        FontWeight->Bold],
       TraditionalForm],
      TraditionalForm], "2"],
    TraditionalForm]], TraditionalForm]], "Output",
 ImageSize->{82, 44},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]=",
 CellID->1545941508]
}, Open  ]],

Cell[TextData[{
 "This calculates integral transformation for any ",
 Cell[BoxData[
  FormBox[
   RowBox[{"\[Integral]", 
    RowBox[{
     SuperscriptBox["d", 
      RowBox[{"D", "-", "1"}]], 
     SubscriptBox["q", "1"], 
     SuperscriptBox["d", 
      RowBox[{"D", "-", "1"}]], 
     SubscriptBox["q", "2"], 
     SuperscriptBox["d", 
      RowBox[{"D", "-", "1"}]], 
     SubscriptBox["q", "3"]}]}], TraditionalForm]]],
 " ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"f", "(", 
     RowBox[{"p", ",", 
      RowBox[{
       SubscriptBox["q", 
        RowBox[{"1", ","}]], 
       SubscriptBox["q", "2"]}], ",", 
      SubscriptBox["q", "3"]}], ")"}], " ", 
    SubsuperscriptBox["q", "1", "i"], 
    SubsuperscriptBox["q", "2", "j"], 
    SubsuperscriptBox["q", "3", "k"]}], TraditionalForm]]],
 "."
}], "Notes",
 CellID->1818046438],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"CTdec", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       SubscriptBox["q", "1"], ",", "i"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       SubscriptBox["q", "2"], ",", "j"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       SubscriptBox["q", "3"], ",", "k"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", "p", "}"}], ",", 
   RowBox[{"List", "\[Rule]", "False"}]}], "]"}]], "Input",
 CellLabel->"In[3]:=",
 CellID->1616776154],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJzt3QlUE9f+B3BBFosIshfZaVRExUK0gFi0oj5R6kItoAWttvpad6kVbatV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    "], {{0, 210}, {534, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{534, 210},
  PlotRange->{{0, 534}, {0, 210}}]], "Output",
 ImageSize->{538, 210},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[3]=",
 CellID->306452316]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Contract", "[", 
   RowBox[{"%", " ", 
    RowBox[{"CVD", "[", 
     RowBox[{"p", ",", "i"}], "]"}], 
    RowBox[{"CVD", "[", 
     RowBox[{"p", ",", "j"}], "]"}], " ", 
    RowBox[{"CVD", "[", 
     RowBox[{"p", ",", "k"}], "]"}]}], "]"}], "//", "Factor"}]], "Input",
 CellLabel->"In[4]:=",
 CellID->663614938],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     FormBox[
      FormBox[
       StyleBox["p",
        StripOnInput->False,
        FontWeight->Bold],
       TraditionalForm],
      TraditionalForm], 
     FormBox["\<\"\[CenterDot]\"\>",
      TraditionalForm], 
     FormBox[
      SubscriptBox[
       FormBox[
        FormBox[
         StyleBox[
          StyleBox["q",
           StripOnInput->False,
           FontWeight->Bold],
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm], 
       FormBox["1",
        TraditionalForm]],
      TraditionalForm]}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     FormBox[
      FormBox[
       StyleBox["p",
        StripOnInput->False,
        FontWeight->Bold],
       TraditionalForm],
      TraditionalForm], 
     FormBox["\<\"\[CenterDot]\"\>",
      TraditionalForm], 
     FormBox[
      SubscriptBox[
       FormBox[
        FormBox[
         StyleBox[
          StyleBox["q",
           StripOnInput->False,
           FontWeight->Bold],
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm], 
       FormBox["2",
        TraditionalForm]],
      TraditionalForm]}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     FormBox[
      FormBox[
       StyleBox["p",
        StripOnInput->False,
        FontWeight->Bold],
       TraditionalForm],
      TraditionalForm], 
     FormBox["\<\"\[CenterDot]\"\>",
      TraditionalForm], 
     FormBox[
      SubscriptBox[
       FormBox[
        FormBox[
         StyleBox[
          StyleBox["q",
           StripOnInput->False,
           FontWeight->Bold],
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm], 
       FormBox["3",
        TraditionalForm]],
      TraditionalForm]}], ")"}]}], TraditionalForm]], "Output",
 ImageSize->{171, 17},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[4]=",
 CellID->1731509272]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["Tdec",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Tdec",
  ButtonNote->"Tdec"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso",
 CellID->119070656]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"CTdec",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 3, 29.766452}", 
    "history" -> {"9.3", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "CTdec[{{qi, a}, {qj, b}, ...}, {p1, p2, ...}] or CTdec[exp, {{qi, a}, \
{qj, b}, ...}, {p1, p2, ...}] calculates the tensorial decomposition formulas \
for Cartesian integrals. The more common ones are saved in TIDL.", 
    "synonyms" -> {}, "tabletags" -> {}, "title" -> "CTdec", "titlemodifier" -> 
    "", "windowtitle" -> "CTdec", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/CTdec"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[6418, 201, 387, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->380288136]},
 "RasterizedOutput"->{
  Cell[12427, 452, 19106, 321, 223, "Output",
   CellTags->"RasterizedOutput",
   CellID->306452316]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 36499, 957},
 {"RasterizedOutput", 36642, 961}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[577, 21, 2980, 74, 53, "AnchorBarGrid",
 CellID->1],
Cell[3560, 97, 282, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[3867, 112, 808, 23, 102, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[4700, 139, 738, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->296209834],
Cell[5441, 165, 31, 0, 14, "SectionHeaderSpacer"],
Cell[CellGroupData[{
Cell[5497, 169, 109, 3, 27, "Input",
 CellID->131732672],
Cell[5609, 174, 748, 20, 75, "Output",
 CellID->1788246199]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[6418, 201, 387, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->380288136],
Cell[CellGroupData[{
Cell[6830, 220, 196, 6, 26, "ExampleSection",
 CellID->1709125748],
Cell[7029, 228, 658, 24, 58, "Notes",
 CellID->76274125],
Cell[CellGroupData[{
Cell[7712, 256, 223, 8, 27, "Input",
 CellID->272441690],
Cell[7938, 266, 1563, 60, 60, "Output",
 CellID->1870429102]
}, Open  ]],
Cell[CellGroupData[{
Cell[9538, 331, 198, 7, 27, "Input",
 CellID->1508196487],
Cell[9739, 340, 1303, 55, 65, "Output",
 CellID->1545941508]
}, Open  ]],
Cell[11057, 398, 847, 31, 62, "Notes",
 CellID->1818046438],
Cell[CellGroupData[{
Cell[11929, 433, 495, 17, 27, "Input",
 CellID->1616776154],
Cell[12427, 452, 19106, 321, 223, "Output",
 CellTags->"RasterizedOutput",
 CellID->306452316]
}, Open  ]],
Cell[CellGroupData[{
Cell[31570, 778, 346, 11, 27, "Input",
 CellID->663614938],
Cell[31919, 791, 2051, 85, 38, "Output",
 CellID->1731509272]
}, Open  ]]
}, Open  ]],
Cell[33997, 880, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34065, 885, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[34338, 899, 195, 8, 56, "SeeAlso",
 CellID->119070656]
}, Open  ]],
Cell[34548, 910, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

